Exploring a quantum theory with graph rewriting and computer algebra. It can be useful to consider complex matrix expressions as circuits, interpreting matrices as parts of a circuit and composition as the “wiring”, or flow of information. This is especially true when describing quantum computation, where graphical languages can vastly reduce the complexity of many calculations. However, manual manipulation of graphs describing such systems quickly becomes untenable for large graphs or large numbers of graphs. To combat this issue, we are developing a tool called Quantomatic, which allows automated and semi-automated explorations of graph rewrite systems and their underlying semantics. We emphasise in this paper the features of Quantomatic that interact with a computer algebra system to discover graphical relationships via the unification of matrix equations. Since these equations can grow exponentially with the size of the graph, we use this method to discover small identities and use those identities as graph rewrites to expand the theory.

References in zbMATH (referenced in 22 articles )

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  1. Coecke, Bob; Horsman, Dominic; Kissinger, Aleks; Wang, Quanlong: Kindergarden quantum mechanics graduates \textit...or how I learned to stop gluing LEGO together and love the ZX-calculus (2022)
  2. de Felice, Giovanni; Toumi, Alexis; Coecke, Bob: DisCoPy: monoidal categories in Python (2021)
  3. Patterson, Evan; Spivak, David I.; Vagner, Dmitry: Wiring diagrams as normal forms for computing in symmetric monoidal categories (2021)
  4. Jeandel, Emmanuel; Perdrix, Simon; Vilmart, Renaud: Completeness of the ZX-calculus (2020)
  5. Kissinger, Aleks; van de Wetering, John: PyZX: large scale automated diagrammatic reasoning (2020)
  6. Miller-Bakewell, Hector: Finite verification of infinite families of diagram equations (2020)
  7. de Felice, Giovanni; Hadzihasanovic, Amar; Ng, Kang Feng: A diagrammatic calculus of fermionic quantum circuits (2019)
  8. Reutter, David Jakob; Vicary, Jamie: Biunitary constructions in quantum information (2019)
  9. Zamdzhiev, Vladimir: A framework for rewriting families of string diagrams (2019)
  10. Bonchi, Filippo; Gadducci, Fabio; Kissinger, Aleks; Sobocinski, Pawel; Zanasi, Fabio: Rewriting with Frobenius (2018)
  11. Hadzihasanovic, Amar; De Felice, Giovanni; Ng, Kang Feng: A diagrammatic axiomatisation of fermionic quantum circuits (2018)
  12. Backens, Miriam; Perdrix, Simon; Wang, Quanlong: A simplified stabilizer ZX-calculus (2017)
  13. Kissinger, Aleks; Quick, David: Tensors, !-graphs, and non-commutative quantum structures (2016)
  14. Lin, Yuhui; Grov, Gudmund; Arthan, Rob: Understanding and maintaining tactics graphically OR how we are learning that a diagram can be worth more than 10K LoC (2016)
  15. Kissinger, Aleks; Zamdzhiev, Vladimir: Quantomatic: a proof assistant for diagrammatic reasoning (2015)
  16. Quick, David: Encoding !-tensors as !-graphs with neighbourhood orders (2015)
  17. Duncan, Ross; Lucas, Maxime: Verifying the Steane code with Quantomatic (2014)
  18. Coecke, Bob; Spekkens, Robert W.: Picturing classical and quantum Bayesian inference (2012)
  19. Coecke, Bob; Duncan, Ross: Interacting quantum observables: categorical algebra and diagrammatics (2011)
  20. Horsman, Clare: Quantum picturalism for topological cluster-state computing (2011)

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Further publications can be found at: https://sites.google.com/site/quantomatic/publications